You are running a local fair, and one of booths has a prize wheel with 12...

You are running a local fair, and one of booths has a prize wheel with 12 slots: 4 light bulbs, 4 gear shifts, and 4 dollar signs. You have been called over to arbitrate a dispute. A customer says that they have been watching the prize wheel spin for an hour, and after 60 spins, they have seen the gear shift come up 24 times (the gear shift means that instead of winning a prize, the customer has to donate work time to the fair). The customer is claiming that that wheel is loaded in favor of the gear shift, and is a cheap way to lure unsuspecting people into doing volunteer work for your fair. What a terrible accusation! How will you save the reputation of your fair? You decide to run a p-test.

• State your Null Hypothesis:

• State your Alternative Hypothesis:

• Given the following p-test, what is your p-value?

Are these results statistically significant? Do you accept or reject the null hypothesis? How can you defend the reputation of your fair?

Expert Solution

Null Hypothesis H0: True proportion of occurrence of gear shift is 1/3 or 0.33.

Alternative Hypothesis Ha: True proportion of occurrence of gear shift is greater than 1/3 or 0.33.

Standard error of proportion SE = = 0.0607042

Sample proportion, = 24/60 = 0.4

Test statistic z = ( - p)/ SE = (0.4 - 0.33)/0.0607042 = 1.15

p-value = P(z > 1.15) = 0.1251

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that these results are not statistically significant and there is no strong evidence that true proportion of occurrence of gear shift is greater than 1/3. Thus, we can defend the reputation of your fair by stating that there is no significant evidence from the data that the wheel is loaded in favor of the gear shift.

orchestra answered 2 years ago

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